Statistical Associating Fluid Theory Model Research Articles

Modeling Dipolar Molecules with PCP-SAFT: A Vector Group-Contribution Method.

Predicting thermodynamic equilibrium properties is essential to develop chemical and energy conversion processes in the absence of experimental data. For the modeling of thermodynamic properties, statistical associating fluid theory (SAFT)-based equations of state, such as perturbed-chain polar (PCP)-SAFT, have been proven powerful and found broad application. The PCP-SAFT parameters can be predicted by group-contribution (GC) methods. However, their application to the dipole term is substantially limited: current GC methods neglect the dipole term or only allow for a single dipolar group per substance to avoid handling the molecular dipole moment's symmetry effects. Still, substances with multiple dipolar groups are highly relevant, and their description substantially improves by including the dipole term in SAFT models. To overcome these limitations, this work proposes a vector-addition-based (Vector-)GC method for the dipole term of PCP-SAFT that accounts for molecular symmetry. The Vector-GC employs information on the substance's molecular 3D structure to predict the molecular dipole moment through a vector addition of bond contributions. Combining the proposed sum rule for dipole moments with established sum rules for the remaining parameters yields a consistent GC method for PCP-SAFT for dipolar substances. The prediction capabilities of the Vector-GC method are analyzed against experimental data for two substance classes: nonassociating oxygenated and halogenated substances. We demonstrate that the Vector-GC method improves vapor pressure and liquid density predictions compared to neglecting the dipole term. Moreover, we show that the Vector-GC method enables differentiation between cis- and trans-isomers. The Vector-GC method, hence, substantially increases the predictive capabilities and applicability domain of GC methods. All parameters are provided as JSON and CSV files, and the Vector-GC method is available through an open-source python package. Additionally, the developed regression framework for GC methods for PCP-SAFT is openly available. The regression framework can be employed to regress the Vector-GC method to other substance classes and is easily adaptable to other sum rules for PCP-SAFT.

Deriving force fields with a multiscale approach: From ab initio calculations to molecular-based equations of state.

Using theoretical and computational tools for predicting thermophysical properties of fluid systems and the soft matter has always been of interest to the physical, chemical, and engineering sciences. Certainly, the ultimate goal is to be able to compute these macroscopic properties from first-principles calculations beginning with the very atomic constitution of matter. In this work, Mie potential parameters were obtained through dimer interaction energy curves derived from ab initio calculations to represent methane and substituted-methane molecules in a spherical one-site coarse-grained model. Bottom-up-based Mie potential parameters of this work were compared with top-down-based ones from the statistical associating fluid theory (SAFT) models for the calculation of thermodynamic properties and critical point by molecular dynamics simulations and SAFT-VR Mie equation of state. Results demonstrated that bottom-up-based Mie potential parameters when averaging the Mie potential parameters of a representative population of conformers provide values close to the top-down-based ones from SAFT models and predict well properties of tetrahedral molecules. This shows the level of consistency embedded in the SAFT-VR Mie family of models and confers the status of a purely predictive equation of state for SAFT-VR Mie when a reasonable model is considered to represent a molecule of interest.

Equationof state and Helmholtz energy functional for fused heterosegmented hard chains.

Modern equationsof state for real nonspherical molecules are often based on Wertheim's first-order thermodynamic perturbation theory (TPT1). A major drawback of TPT1 is that it assumes tangentially bonded spheres. In this work, we develop a Helmholtz energy functional for systems comprising hard heterosegmented chains with arbitrary bond lengths. This is achieved by using hard-sphere fragments (i.e., hard spheres with spherical caps removed at the intersection to their neighbors) as monomers as opposed to full hard spheres. The model is written as a Helmholtz energy functional for inhomogeneous systems and the equationof state for a homogeneous system is determined as a special case. We thereby obtain an equationof state that can be used as a reference to develop statistical associating fluid theory models that more accurately describe the thermodynamic properties of nonspherical molecules. The model is validated against molecular simulation results of bulk pressures and density profiles in slit pores. For the bulk pressures, we show that the equationof state is in excellent agreement with results from molecular simulation for dimers, trimers, and chains of up to 20 segments. The density profiles of individual segments of the chains are regarded in slit pores. Some deviations of the theory from results of molecular simulations are observed for strongly fused chains. Overall, however, good agreement is found for inhomogeneous systems.

Application of the Corresponding-State Law to the Parametrization of Statistical Associating Fluid Theory (SAFT)-Type Models: Generation and Use of “Generalized Charts”

Most of the Statistical Associating Fluid Theory (SAFT) and cubic equations of state (EoS) for nonassociating pure components obey the three-parameter corresponding-state law, meaning that the knowledge of three component-specific properties is a prerequisite to apply an EoS to a given pure species. Here, the methodology used to attribute values to EoS parameters is called “parameterization procedure”. In this Article, it is shown that generalized charts, derived from the corresponding-state theory, can be used advantageously to parametrize SAFT models. SAFT EoS is a well-established class of models frequently used for process simulation. Depending on the EoS parameter set selected, most of SAFT EoS are likely to predict unrealistic phenomena (mainly, the presence of multiple critical points and three-fluid phase equilibrium regions in pure-component phase diagrams). Generalized charts can be used to detect whether such unrealistic phenomena affect pure-component phase diagrams in the temperature and pressure domains of interest. As a second application, it is proposed to parametrize SAFT EoS in the same spirit as cubic EoS: the three SAFT input parameters are fixed in order to exactly reproduce the experimental critical temperature, critical pressure, and one point of the vaporization curve through the acentric factor. It is shown that the procedure is simple to implement and opens the door to a large industrialization of SAFT EoS (i.e., the possibility to determine SAFT input parameters for any compound using a universal and univocal method).

Integrated solvent and process design for continuous crystallization and solvent recycling using PC‐SAFT

Solvent usage is a major source of environmental waste in pharmaceutical industry. The current paradigm shift toward continuous manufacturing in pharmaceutical industry has renewed the interest in continuous crystallization, which offers the prospect of easy solvent recycling. However, the selection of solvents for an integrated crystallization processes is nontrivial due to the likely trade‐off between optimal solvent properties for crystallization and solvent separation and recycling. A systematic approach for the simultaneous optimization of process conditions and solvent selection for continuous crystallization including solvent recycling is presented. A unified perturbed‐chain statistical associating fluid theory model framework is applied to predict thermodynamic properties related to solubility and vapor‐liquid equilibrium, which is integrated with a process model. A continuous mapping procedure is adopted to solve the optimization problem effectively. A case study based on continuous antisolvent crystallization of paracetamol with solvent separation via flash demonstrates the approach. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1205–1216, 2018

Measurement and Modeling of High Pressure Vapor–Liquid Equilibrium for Methyl Acetate or Ethyl Acetate with 2-Butanol. Isobaric Data at 1.5 MPa

Vapor–liquid equilibrium data for the binary systems methyl acetate + 2-butanol and ethyl acetate+2-butanol, have been determined at 1.5 MPa employing a metal ebulliometer with recirculation of both phases. The thermodynamic consistency of experimental data has been verified with the Van Ness point-to-point test, using the routine in Fortran proposed by Fredenslund et al. in which the second and third virial coefficients were calculated using the Tsonopoulos method and the Orbey and Vera procedure, respectively. Different group contribution models were employed for prediction of high pressure data. The UNIFAC–Lyngby model returned good overall predictions. The ϕ–ϕ approach was applied using the perturbed-chain statistical associating fluid theory model. This equation of state produces an acceptable agreement between experimental and calculated data in both systems.

Modeling of CO2 solubility in single and mixed electrolyte solutions using statistical associating fluid theory

Statistical associating fluid theory (SAFT) is used to model CO2 solubilities in single and mixed electrolyte solutions. The proposed SAFT model implements an improved mean spherical approximation in the primitive model to represent the electrostatic interactions between ions, using a parameter K to correct the excess energies (“KMSA” for short). With the KMSA formalism, the proposed model is able to describe accurately mean ionic activity coefficients and liquid densities of electrolyte solutions including Na+, K+, Ca2+, Mg2+, Cl−, Br− and SO42− from 298.15K to 473.15K using mostly temperature independent parameters, with sole exception being the volume of anions. CO2 is modeled as a non-associating molecule, and temperature-dependent CO2–H2O and CO2–ion cross interactions are used to obtain CO2 solubilities in H2O and in single ion electrolyte solutions. Without any additional fitting parameters, CO2 solubilities in mixed electrolyte solutions and synthetic brines are predicted, in good agreement with experimental measurements.

Prediction of the critical properties of n-alkanes and their mixtures with two versions of SAFT equation of state

Two versions of statistical associating fluid theory (SAFT) equation of state (EoS), namely modified SAFT-BACK and original SAFT, were used to calculate the critical temperatures and pressures of 10 n-alkanes (from $$c_{1}$$ to $$c_{10}$$ ). The obtained results were compared with the available experimental data to assess the predictive power of these EoSs in the critical region. The absolute average percentage deviation (AAD %) of the results obtained from the modified SAFT-BACK model indicated that this EoS had a good performance in the prediction of the critical points of the n-alkanes, but the deviation resulting from the original SAFT EoS reflected the limitations of the latter EoS in representing the critical region. Moreover, the critical temperatures for binary mixtures of n-alkane were calculated using both the original SAFT and the modified SAFT-BACK models and the results were compared with the data predicted by the correlation relations. The modified SAFT-BACK model showed a very good performance, while the original SAFT model did not yield an appropriate prediction of the critical temperatures of n-alkane binary mixtures.

Liquid–Liquid Equilibrium of Associating Fluid Mixtures Using Perturbed-Hard-Sphere-Chain Equation of State Combined with the Association Model

Perturbed-hard-sphere-chain-association (PHSC-AS) equation of state, which is defined by incorporating the association term of the statistical associating fluid theory (SAFT) model into the PHSC equation of state with van der Waals-type dispersion term, is used to calculate the liquid–liquid equilibrium (LLE) for complex associating mixtures such as alcohol/alkane, water/alkane, acetic acid/alkane, alcohol/water, and carboxylic acid/water systems. In this work, the PHSC-AS models with two different chain terms have been investigated. One is the original model proposed by Song et al. [Macromolecules 1994, 27 (2), 441−448], and the other is the modified model whose chain term was replaced with that of the SAFT model. The calculated results of LLE for associating mixtures are compared with those by the purturbed-chain-SAFT (PC-SAFT) model as well. The results with PHSC-AS and PC-SAFT equation of state are in acceptable agreement with the experimental data. Despite the simple dispersion equation with van der Waals-type, PHSC-AS models show a reasonable calculation performance for LLE of associating fluid mixture.

High-pressure vapor–liquid equilibria of methanol + propylene: Experimental and modeling with SAFT

The high-pressure vapor–liquid equilibria of methanol+propylene was measured experimentally within a temperature and pressure range of 293–373K and 0.17–3.7MPa, respectively, using a synthetic method. The system showed a highly non-ideal behavior with positive deviation from Raoult's law. The phase behavior was also modeled by the statistical associating fluid theory (SAFT) and the Soave–Redlich–Kwong (SRK) equations of state. The statistical associating fluid theory correlated the phase behavior of the binary system much better than the Soave–Redlich–Kwong model, especially at higher pressures. For example, the average absolute deviation percent (AAD%) at T=370K was 1.11% for the SAFT model with k12=0.02088 and 6.75% for the SRK model with k12=0.08035.

Effect of alcohol on the solubility of amino acid in water

In a previous work, the parameters of the statistical associating fluid theory (SAFT) equation of state for amino acids were determined by using the method developed. The solubility of amino acids in water was modeled. In this work, the SAFT equation of state has been applied to describe the solubility of amino acids in aqueous alcohol solutions. The systems include dl-alanine/ethanol/water, glycine/ethanol/water, dl-valine/ethanol/water, dl-serine/ethanol/water, glycine/1-propanol/water, glycine/2-propanol/water, l-alanine/2-propanol/water, l-leucine/ethanol/water. Binary interaction parameters between amino acid and alcohol are needed by the SAFT model to get good modeling results.

Modeling of water activity, oxygen solubility and density of sugar and sugar alcohol solutions

Water activity, oxygen solubility and density of aqueous solutions of sugar and sugar alcohols have been modeled with the statistical associating fluid theory (SAFT). The modeling is accomplished by extending the previously developed method to determine the SAFT parameters for sugar and sugar alcohols. For the aqueous solutions of sorbitol/water, xylitol/water, mannitol/water, xylitol/sorbitol/water and xylitol/mannitol/water, the water activity has been predicted. The solubilities of oxygen in water and in aqueous solutions of glucose/water, fructose/water, sucrose/water, maltose/water and mannitol/water have been modeled. The density predictions for mannitol/sucrose/water, mannitol/sorbitol/water and mannitol/sorbitol/sucrose/water have been carried out. All the modeling results show that, by using the previously developed method to determine the SAFT parameters, the SAFT model has been able to model the water activity, oxygen solubility and density with very good accuracy, and the SAFT model can be taken as a suitable tool for describing sugar and sugar containing solutions.

A quasi-chemical nonrandom lattice fluid model for phase equilibria of associating systems

The contribution from Veytsman statistics for associating is combined with the quasi-chemical nonrandom lattice fluid (QLF) equation of state developed by the present authors. The physical contribution is characterized by temperature independent molecular parameters, representing close packed volume of a mer, segment numbers and energy parameters of a pure fluid, and a binary interaction parameter for a mixture. The chemical part is represented by the internal energy and entropy of the associating system. The resulting quasi-chemical nonrandom associating lattice fluid equation of state was applied to describe thermodynamic properties of pure fluids and phase equilibria of mixtures. The absolute chemical potentials which are derived from the canonical partition function are presented by using the fundament thermodynamic relations to consistently calculate phase equilibrium properties. The results for alkane–alkanol and alcohol–alkanol mixtures were found satisfactory for most systems when compared with the quasi-chemical nonrandom lattice fluid model and the statistical associating fluid theory model.

Density Calculation of Sugar Solutions with the SAFT Model

Density is one of the key physicochemical properties for sugar solutions. The objective of this work is to model the density of sugar solutions. The density calculation has been carried out by applying statistical associating fluid theory (SAFT) equations of state. This new method made use of critical temperature, pressure, and volume as well as normal boiling temperature to determine the SAFT parameters for sugars and is now extended to determine the SAFT parameters for d-xylose, sucrose, and sorbitol. The critical properties and normal boiling temperature of sugars are estimated based on information of molecular structure. The densities of sugar solutions including binary systems of d-glucose/H2O, d-fructose/H2O, d-xylose/H2O, sucrose/H2O, and sorbitol/H2O; ternary systems of d-fructose/H2O/ethanol and sucrose/sorbitol/H2O; and quaternary systems of d-glucose/d-fructose/H2O/ethanol have been calculated without using binary interaction parameters. Results with high accuracy have been obtained. Finally, t...

Evaluation of SAFT and PC-SAFT models for the description of homo- and co-polymer solution phase equilibria

Statistical associating fluid theory (SAFT) and perturbed-chain SAFT (PC-SAFT) are used to model the phase behavior of polymer–solvent mixtures over a wide temperature and pressure range. Homopolymers (polyolefins) as well as co-polymers are examined. Calculations were performed using various recently proposed robust algorithms for polydisperse polymers. Various polymer properties that affect substantially the phase behavior, such as molecular weight, polydispersity, and macromolecular architecture, were considered. For most of the systems examined, PC-SAFT correlation is marginally closer to experimental data than SAFT. Nevertheless, there are a number of mixtures where SAFT is the preferred model.

Application of the SAFT equation of state to biomass fast pyrolysis liquid

A practical method has been developed for determining parameters for the statistical associating fluid theory (SAFT) equation of state. Critical temperature, pressure, and density as well as normal boiling point are used to determine parameters for associating compounds, especially sugars. The method has been verified by the description of sugar solubilities in water and in mixed solvents. The predicted and correlated results are in good agreement with the experimental data of systems containing D-fructose, D-glucose, and sucrose. The SAFT model has been further applied to a sugar-containing system in modeling of the recovery of chemicals, such as the sugars levoglucosan and hydroxyacetaldehyde, from a pyrolysis liquid produced from biomass fast pyrolysis. At high temperatures, the two sugars are instable. The modeling of separation of the sugars has been carried out at temperatures 50 °C and 60 °C and in a pressure range of 0.01–0.03 bar. Under these conditions, the effect of pressure on the separation is larger than that of temperature. A lower pressure and a higher water content of the pyrolysis liquid are favourable for the separation. With pressure decreasing, the effect of water content on the separation is becoming less significant.

Group contribution method with SAFT EOS applied to vapor liquid equilibria of various hydrocarbon series

A new group contribution method is proposed using the statistical associating fluid theory (SAFT) equation of state (EOS), in order to describe the thermodynamic properties of hydrocarbon series. The method is developed for vapor–liquid equilibrium (VLE) calculations for a large number of hydrocarbons, with the use of several group parameters. SAFT models are chosen for the physical meaning of their parameters. These can be related to the molecular structure. Two versions of the SAFT EOS are used in this work: the original SAFT equation of state, proposed by Chapman et al. [Ind. Eng. Chem. Res. 29 (1990) 1709] and SAFT variable range (SAFT-VR) equation of state, proposed by Gil-Villegas et al. [J. Chem. Phys. 106 (1997) 4168]. The present group contribution method consists in calculating the equation of state parameters (dispersion energy ε, segment diameter σ, chain length m and square-well range parameter λ for SAFT-VR) using group contribution rules. In this paper, we have treated pure compounds of five hydrocarbon families: n-alkanes, alkyl-benzenes, alkyl-cyclohexanes, α-olefins and 1-alkanols. The results obtained are compared with those of the usual approach (fitting the molecular parameters of each compound on its own properties) and seem to be nearly equivalent. The results of the present method are comparable with those of other predictive approaches.

Reliable Computation of Phase Stability and Equilibrium from the SAFT Equation of State

In recent years, molecularly based equations of state, as typified by the SAFT (statistical associating fluid theory) approach, have become increasingly popular tools for the modeling of phase behavior. However, whether this, or even a much simpler model, is used, the reliable calculation of phase behavior from a given model can be a very challenging computational problem. A new methodology is described that is the first completely reliable technique for computing phase stability and equilibrium from the SAFT model. The method is based on interval analysis, in particular an interval Newton/generalized bisection algorithm, that provides a mathematical and computational guarantee of reliability and is demonstrated using nonassociating, self-associating, and cross-associating systems. New techniques are presented that can also be exploited when conventional point-valued solution methods are used. These include the use of a volume-based problem formulation, in which the core thermodynamic function for phase equilibrium at constant temperature and pressure is the Helmholtz energy, and an approach for dealing with the internal iteration needed when there are association effects. This approach provides for direct, as opposed to iterative, determination of the derivatives of the internal variables.

Simplified crossover SAFT equation of state for pure fluids and fluid mixtures

A simplified modification of the crossover statistical associating fluid theory (SAFT) EOS is used to describe thermodynamic properties of pure fluids and binary mixtures over a wide range of parameters of state including the nearest vicinity of the critical point. For pure fluids, the simplified crossover (SCR) SAFT model contains only three adjustable parameters but allows an accurate prediction of the critical parameters of pure fluids and yields a better representation of the thermodynamic properties of pure fluids than the original SAFT equation of state. For binary mixtures, simple mixing rules with only one adjustable parameter are used. A comparison is made with experimental data for pure refrigerants R12, R22, R32, R125, R134a, R143a, and mixtures R22+R12, R32+R134a and R125+R32 in the one- and two-phase regions. The SCR SAFT EOS reproduces the saturated pressure data with an average absolute deviation (AAD) of about 1.1% and the saturated liquid densities with an AAD of about 0.9%. In the one-phase region, the SCR SAFT equation represents the experimental values of pressure with an AAD of about 2.2% in the range of temperatures and density bounded by T≥Tc and ρ≤2ρc.

Comparison of Perturbed Hard-Sphere-Chain Theory with Statistical Associating Fluid Theory for Square-Well Fluids

The effect of hard-sphere-chain equations on the description of phase behavior is presented by the comparison of perturbed hard-sphere-chain (PHSC) theory with statistical associating fluid theory (SAFT) for square-well fluids. The PHSC-type equation of this work is based on the hard-sphere-chain equation of Chiew (PY−CS), the square-well fluid model of Alder et al., and the expression of Chen and Kreglewski. The PHSC-type equation has expressions similar to those of the SAFT equation. A comparison of the PHSC-type equation with the SAFT model shows that the PHSC-type equation of state presents slightly better results of pure compounds and much better vapor−liquid equilibrium results of high-concentration polymer solutions.